Answer:
551 people
Explanation:
We have that for this type of situation the equation that models the population depending on the time is:
P (t) = I * e ^ (k * t)
Where I is the initial population, that is to say that for this case it would be:
P (t) = 500 * e ^ (k * t)
k is the constant of proportionality and t the time, they tell us that in 10 years it increases 5%, therefore the population would be:
500 + 500 * 0.05 = 525, therefore:
525 = 500 * e ^ (k * 10)
we solve:
525/500 = e ^ (k * 10)
ln 1.05 = k * 10
k = 0.00488
Now, to calculate how much the population is in 20 years it would be:
P (t) = 500 * e ^ (0.00488 * 20)
P (t) = 551.26
In other words, the population would be approximately 551 people